Authors:
(1) Mengshuo Jia, Department of Information Technology and Electrical Engineering, ETH Zürich, Physikstrasse 3, 8092, Zürich, Switzerland;
(2) Gabriela Hug, Department of Information Technology and Electrical Engineering, ETH Zürich, Physikstrasse 3, 8092, Zürich, Switzerland;
(3) Ning Zhang, Department of Electrical Engineering, Tsinghua University, Shuangqing Rd 30, 100084, Beijing, China;
(4) Zhaojian Wang, Department of Automation, Shanghai Jiao Tong University, Dongchuan Rd 800, 200240, Shanghai, China;
(5) Yi Wang, Department of Electrical and Electronic Engineering, The University of Hong Kong, Pok Fu Lam, Hong Kong, China;
(6) Chongqing Kang, Department of Electrical Engineering, Tsinghua University, Shuangqing Rd 30, 100084, Beijing, China. Table of Links Abstract and 1. Introduction 2. Evaluated Methods 3. Review of Existing Experiments 4. Generalizability and Applicability Evaluations and 4.1. Predictor and Response Generalizability 4.2. Applicability to Cases with Multicollinearity and 4.3. Zero Predictor Applicability 4.4. Constant Predictor Applicability and 4.5. Normalization Applicability 5. Numerical Evaluations and 5.1. Experiment Settings 5.2. Evaluation Overview 5.3. Failure Evaluation 5.4. Accuracy Evaluation 5.5. Efficiency Evaluation 6. Open Questions 7. Conclusion Appendix A and References 3. Review of Existing Experiments Before conducting evaluations of the methods listed in Table 1, we here aim to offer a detailed review of existing DPFL experiments in the literature, as depicted in Table 2. This review intends to present the experimental accomplishments of previous DPFL studies, while simultaneously revealing the importance and need for an extensive numerical comparison of all DPFL methods. Below are the further discussions of Table 2. Firstly, Table 2 indicates that both transmission and distribution grids were used as test cases to verify DPFL methods. While distribution grids differ from transmission grids in terms of symmetry and topology, DPFL methods are generally applicable to both types of systems, such as the methods in [15, 12, 30, 21, 11]. The reasons are twofold. First, even if the three phases in distribution systems are unbalanced, DPFL methods can still be implemented by either training one DPFL model for each phase [52], or training an overall DPFL model for all variables in three phases [22, 11, 12, 24]. Note that the latter can generate a DPFL model reflecting the mutual influences between phases. Second, from a DPFL perspective, radial topologies do not pose any unique challenges compared to mesh topologies, as the difference is only in the number of dependent and independent variables. In summary, while distribution grids may have unbalanced characteristics and radial topologies, these attributes do not bring special difficulties to DPFL studies. Secondly, Table 2 reveals that many evaluations solely depended on artificial data for training and testing, without considering the effects of noise and outliers on the data. This ideal testing environment is rarely found in real life, and the resulting conclusions may not hold in practice. To address this issue, it is recommended that synthetic data be injected with noise and outliers to mimic real-world scenarios. Thirdly, as indicated in Table 2, only a few studies report the load fluctuation range used in their simulations. This is worth mentioning because the accuracy of the DPFL model is highly dependent on the simulated fluctuations. E.g., a narrow fluctuation range typically leads to higher accuracy for the DPFL model. Without this information being made public, it is difficult to determine the reason for the high accuracy of the evaluated DPFL model. Finally, Table 2 indicates which of the DPFL approaches have been evaluated in existing DPFL studies. These evaluations aimed to implement a comparative analysis between established and novel DPFL methods at that time. However, the scope of these comparisons is quite narrow, with only a few DPFL studies undertaking evaluations against a limited number of existing DPFL approaches (some works only conducted comparisons with PPFL methods). Such constrained comparisons fail to provide an in-depth understanding of the overall performance of DPFL methods. Consequently, a more exhaustive and inclusive comparison across all the DPFL approaches is clearly needed, in order to demonstrate their relative merits and limitations comprehensively. This paper is available on arxiv under CC BY-NC-ND 4.0 Deed (Attribution-Noncommercial-Noderivs 4.0 International) license. Authors: (1) Mengshuo Jia, Department of Information Technology and Electrical Engineering, ETH Zürich, Physikstrasse 3, 8092, Zürich, Switzerland; (2) Gabriela Hug, Department of Information Technology and Electrical Engineering, ETH Zürich, Physikstrasse 3, 8092, Zürich, Switzerland; (3) Ning Zhang, Department of Electrical Engineering, Tsinghua University, Shuangqing Rd 30, 100084, Beijing, China; (4) Zhaojian Wang, Department of Automation, Shanghai Jiao Tong University, Dongchuan Rd 800, 200240, Shanghai, China; (5) Yi Wang, Department of Electrical and Electronic Engineering, The University of Hong Kong, Pok Fu Lam, Hong Kong, China; (6) Chongqing Kang, Department of Electrical Engineering, Tsinghua University, Shuangqing Rd 30, 100084, Beijing, China. Authors: Authors: (1) Mengshuo Jia, Department of Information Technology and Electrical Engineering, ETH Zürich, Physikstrasse 3, 8092, Zürich, Switzerland; (2) Gabriela Hug, Department of Information Technology and Electrical Engineering, ETH Zürich, Physikstrasse 3, 8092, Zürich, Switzerland; (3) Ning Zhang, Department of Electrical Engineering, Tsinghua University, Shuangqing Rd 30, 100084, Beijing, China; (4) Zhaojian Wang, Department of Automation, Shanghai Jiao Tong University, Dongchuan Rd 800, 200240, Shanghai, China; (5) Yi Wang, Department of Electrical and Electronic Engineering, The University of Hong Kong, Pok Fu Lam, Hong Kong, China; (6) Chongqing Kang, Department of Electrical Engineering, Tsinghua University, Shuangqing Rd 30, 100084, Beijing, China. Table of Links Abstract and 1. Introduction Abstract and 1. Introduction 2. Evaluated Methods 3. Review of Existing Experiments 3. Review of Existing Experiments 4. Generalizability and Applicability Evaluations and 4.1. Predictor and Response Generalizability 4. Generalizability and Applicability Evaluations and 4.1. Predictor and Response Generalizability 4.2. Applicability to Cases with Multicollinearity and 4.3. Zero Predictor Applicability 4.2. Applicability to Cases with Multicollinearity and 4.3. Zero Predictor Applicability 4.4. Constant Predictor Applicability and 4.5. Normalization Applicability 4.4. Constant Predictor Applicability and 4.5. Normalization Applicability 5. Numerical Evaluations and 5.1. Experiment Settings 5. Numerical Evaluations and 5.1. Experiment Settings 5.2. Evaluation Overview 5.2. Evaluation Overview 5.3. Failure Evaluation 5.3. Failure Evaluation 5.4. Accuracy Evaluation 5.4. Accuracy Evaluation 5.5. Efficiency Evaluation 5.5. Efficiency Evaluation 6. Open Questions 6. Open Questions 7. Conclusion 7. Conclusion Appendix A and References Appendix A and References 3. Review of Existing Experiments Before conducting evaluations of the methods listed in Table 1, we here aim to offer a detailed review of existing DPFL experiments in the literature, as depicted in Table 2. This review intends to present the experimental accomplishments of previous DPFL studies, while simultaneously revealing the importance and need for an extensive numerical comparison of all DPFL methods. Below are the further discussions of Table 2. Firstly, Table 2 indicates that both transmission and distribution grids were used as test cases to verify DPFL methods. While distribution grids differ from transmission grids in terms of symmetry and topology, DPFL methods are generally applicable to both types of systems, such as the methods in [15, 12, 30, 21, 11]. The reasons are twofold. First, even if the three phases in distribution systems are unbalanced, DPFL methods can still be implemented by either training one DPFL model for each phase [52], or training an overall DPFL model for all variables in three phases [22, 11, 12, 24]. Note that the latter can generate a DPFL model reflecting the mutual influences between phases. Second, from a DPFL perspective, radial topologies do not pose any unique challenges compared to mesh topologies, as the difference is only in the number of dependent and independent variables. In summary, while distribution grids may have unbalanced characteristics and radial topologies, these attributes do not bring special difficulties to DPFL studies. Secondly, Table 2 reveals that many evaluations solely depended on artificial data for training and testing, without considering the effects of noise and outliers on the data. This ideal testing environment is rarely found in real life, and the resulting conclusions may not hold in practice. To address this issue, it is recommended that synthetic data be injected with noise and outliers to mimic real-world scenarios. Thirdly, as indicated in Table 2, only a few studies report the load fluctuation range used in their simulations. This is worth mentioning because the accuracy of the DPFL model is highly dependent on the simulated fluctuations. E.g., a narrow fluctuation range typically leads to higher accuracy for the DPFL model. Without this information being made public, it is difficult to determine the reason for the high accuracy of the evaluated DPFL model. Finally, Table 2 indicates which of the DPFL approaches have been evaluated in existing DPFL studies. These evaluations aimed to implement a comparative analysis between established and novel DPFL methods at that time. However, the scope of these comparisons is quite narrow, with only a few DPFL studies undertaking evaluations against a limited number of existing DPFL approaches (some works only conducted comparisons with PPFL methods). Such constrained comparisons fail to provide an in-depth understanding of the overall performance of DPFL methods. Consequently, a more exhaustive and inclusive comparison across all the DPFL approaches is clearly needed, in order to demonstrate their relative merits and limitations comprehensively. This paper is available on arxiv under CC BY-NC-ND 4.0 Deed (Attribution-Noncommercial-Noderivs 4.0 International) license. This paper is available on arxiv under CC BY-NC-ND 4.0 Deed (Attribution-Noncommercial-Noderivs 4.0 International) license. available on arxiv

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